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URL: https://oeis.org/A200787

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A200787
Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases.
1
32, 216, 840, 2425, 5796, 12152, 23136, 40905, 68200, 108416, 165672, 244881, 351820, 493200, 676736, 911217, 1206576, 1573960, 2025800, 2575881, 3239412, 4033096, 4975200, 6085625, 7385976, 8899632, 10651816, 12669665, 14982300
OFFSET
1,1
COMMENTS
Row 3 of A200785.
LINKS
FORMULA
Empirical: a(n) = (7/12)*n^5 + (47/12)*n^4 + (39/4)*n^3 + (133/12)*n^2 + (17/3)*n + 1.
Conjectures from Colin Barker, Oct 15 2017: (Start)
G.f.: x*(32 + 24*x + 24*x^2 - 15*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = (1 + n)^2*(12 + 44*n + 33*n^2 + 7*n^3) / 12 .
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
EXAMPLE
Some solutions for n=3
..2....1....3....2....2....3....1....3....1....1....2....1....0....1....2....0
..0....0....3....3....1....2....3....1....3....2....0....0....3....3....2....0
..0....1....1....3....3....1....3....1....0....0....0....2....3....2....3....0
..3....1....1....1....1....0....3....2....3....3....3....2....1....1....0....0
..0....1....1....0....2....3....3....1....1....0....1....0....3....1....2....3
CROSSREFS
Sequence in context: A125342 A126500 A160538 * A250354 A183778 A146089
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 22 2011
STATUS
approved